Signalers optimize costs and benefits

Signals (at least those specialized for communication) always have costs, regardless of whether or not they are honest.   Furthermore, all signalers get the same benefit for the same effort -- "equal pay for equal work" applies to communication.   Because receivers respond to signals, not to the true state of the signaler, similar signals get similar responses, regardless of their origin.   Of course, honest signals truly reflect the states of the signalers.   A receiver has no way of confirming in any particular instance whether or not a signal is honest.   Signalers should evolve to optimize their threshold for response and then respond whenever the level of activity in their sense organs reaches this threshold.

Signalers cannot control whether or not a receiver will respond or not, in any absolute way, but signals that are more powerful, repetitive, and conspicuous (contrast more with background energy) are more likely to exceed a receiver's threshold.   More signal is likely to produce more response.

Because producing a signal always involves some cost (at least for signals specialized for communication, those without other uses for the signaler), more signal requires more cost.   How should signalers balance costs of signaling and benefits from responses?

More signal, we just agreed, requires more cost.   Suppose costs of signals are mostly decreased survival (less time feeding and more exposure to predators).   The chance of survival (S = 1 - mortality) is then a steadily dereasing function of the amount of signal a signaler produces.

More signal produces more response.   Suppose the benefits to the signaler of the intended receiver's responses are mostly increased reproduction (greater chances of attracting a mate).   The expected reproductive success (RS) is a steadily increasing function of the amount of signal.

Since the spread of genes depends both of survival of individuals and their reproduction, the product of survival and reproductive success (S X RS) is a good measure of the potential spread of an individual's alleles.   This product must be near or at zero when a signaler produces only a little signal (RS equal to or near 0).   Also for high levels of signal, this product must approach or equal zero (S equal to or near 0).   At some intermediate level of signal, S X RS must reach a maximum.   This level of signaling maximizes the spread of the signaler's alleles.

Another signaler might have lower condition than the first.   Its survival (S) is lower than the first for every level of signaling (it's hard to imagine how it could be otherwise).   On the other hand, the benefit of any level of signaling is exactly the same for both individuals (remember that receivers only respond to the signal, not to the true state of the signaler).   This second signaler also does best at a signal level that maximizes his S X RS.   Because his S is lower than the first individual's, his maximum product occurs at a lower level of signal.   If the second individual produced more signal, it would lower its S X RS and thus the spread of its alleles.

So individuals that differ in condition in this way have different levels of signaling that maximize the spread of their alleles.   Furthermore, the optimal level of signaling for each individual corresponds exactly to its condition.   Signals honestly reflect the states of the signalers.

So far we have seen that receivers must optimize their thresholds in accordance with the inevitable trade-offs between errors and correct responses to signals.   Also, signalers must optimize their level of signaling in accordance with the rising costs of increased signaling.

It gets more complicated yet ...

  • The optimal level of signal for signalers affects the signal/noise ratio for receivers and hence affects their optimal threshold
and
  • the optimal threshold for receivers affects the benefits for signalers for any level of signaling and hence affects the optimal level of signaling by signalers.

The final question thus is this ... is there some joint optimum for both signalers and receivers at which neither one can do better?   Or is this interaction of optimal receivers and optimal signalers too complicated a problem for evolution (or mathematics) to solve?

The answer is yes ... there is a joint optimum in the evolution of communication.   Signalers and receivers should evolve to a single interdependent pair of optima for the level of signaling and the threshold for response.   At this joint optimum, signals do not always evoke responses from intended receivers (tough luck for signalers), and receivers do not always avoid mistakes (tough luck for receivers).   Signalers are vulnerable to eavesdropping.   Receivers are vulnerable to manipulation.   Nevertheless, at this joint optimum any communication system is honest on average.